using DiffEqBase, OrdinaryDiffEq, DiffEqBiological, DiffEqJump, DiffEqProblemLibrary.JumpProblemLibrary, Plots, Statistics
gr()
fmt = :png
JumpProblemLibrary.importjumpproblems()

Model and example solutions

Here we implement the gene expression model from appendix A.6 of Marchetti, Priami and Thanh, Simulation Algorithms for Comptuational Systems Biology, Springer (2017).

jprob = prob_jump_dnadimer_repressor
rn = jprob.network
rnpar = jprob.rates
varlabels = jprob.prob_data["specs_names"]
u0 = jprob.u0
tf = jprob.tstop

4000.0

u0f = [1000., 0., 0., 0.,0.]
odeprob = ODEProblem(rn, u0f, (0.,tf),rnpar)
sol = solve(odeprob,Tsit5())
plot(sol, format=:png, label=varlabels)

tf      = 4000.
methods = (Direct(),DirectFW(),FRM(),FRMFW(),SortingDirect(),NRM(),DirectCR(),RSSA())
shortlabels = [string(leg)[12:end-2] for leg in methods]
prob    = prob = DiscreteProblem(u0, (0.0, tf), rnpar)
ploth   = plot(reuse=false)
p = []
for (i,method) in enumerate(methods)
    jump_prob = JumpProblem(prob, method, rn, save_positions=(false,false))
    sol = solve(jump_prob, SSAStepper(), saveat=tf/1000.)
    plot!(ploth,sol.t,sol[3,:],label=shortlabels[i], format=fmt)
    push!(p, plot(sol,title=shortlabels[i],leg=false,format=fmt))
end
plot(ploth, title="Protein level", xlabel="time",format=fmt)

plot(p[end],format=fmt,legend=true,labels=varlabels)

Benchmarking performance of the methods

function run_benchmark!(t, jump_prob, stepper)
    sol = solve(jump_prob, stepper)
    @inbounds for i in 1:length(t)
        t[i] = @elapsed (sol = solve(jump_prob, stepper))
    end
end

run_benchmark! (generic function with 1 method)

nsims = 50
benchmarks = Vector{Vector{Float64}}()
for method in methods
    jump_prob = JumpProblem(prob, method, rn, save_positions=(false,false))
    stepper = SSAStepper()
    t = Vector{Float64}(undef, nsims)
    run_benchmark!(t, jump_prob, stepper)
    push!(benchmarks, t)
end

medtimes = Vector{Float64}(undef,length(methods))
stdtimes = Vector{Float64}(undef,length(methods))
avgtimes = Vector{Float64}(undef,length(methods))
for i in 1:length(methods)
    medtimes[i] = median(benchmarks[i])
    avgtimes[i] = mean(benchmarks[i])
    stdtimes[i] = std(benchmarks[i])
end

using DataFrames
df = DataFrame(names=shortlabels,medtimes=medtimes,relmedtimes=(medtimes/medtimes[1]),avgtimes=avgtimes, std=stdtimes, cv=stdtimes./avgtimes)
sa = [text(string(round(mt,digits=3),"s"),:center,12) for mt in df.medtimes]
bar(df.names,df.relmedtimes,legend=:false, fmt=fmt)
scatter!(df.names, .05 .+ df.relmedtimes, markeralpha=0, series_annotations=sa, fmt=fmt)
ylabel!("median relative to Direct")
title!("Marchetti Gene Expression Model")

using DiffEqBenchmarks
DiffEqBenchmarks.bench_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file])

using DiffEqBenchmarks
DiffEqBenchmarks.weave_file("Jumps","NegFeedback_GeneExpr_Marchetti.jmd")

Julia Version 1.3.0
Commit 46ce4d7933 (2019-11-26 06:09 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: Intel(R) Core(TM) i7-9700K CPU @ 3.60GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-6.0.1 (ORCJIT, skylake)

Status: `/home/julialab/.julia/dev/DiffEqBenchmarks/Project.toml`
[28f2ccd6-bb30-5033-b560-165f7b14dc2f] ApproxFun 0.11.8
[a134a8b2-14d6-55f6-9291-3336d3ab0209] BlackBoxOptim 0.5.0
[a93c6f00-e57d-5684-b7b6-d8193f3e46c0] DataFrames 0.20.0
[2b5f629d-d688-5b77-993f-72d75c75574e] DiffEqBase 6.7.0
[eb300fae-53e8-50a0-950c-e21f52c2b7e0] DiffEqBiological 4.1.0
[f3b72e0c-5b89-59e1-b016-84e28bfd966d] DiffEqDevTools 2.16.0
[c894b116-72e5-5b58-be3c-e6d8d4ac2b12] DiffEqJump 6.3.0
[1130ab10-4a5a-5621-a13d-e4788d82bd4c] DiffEqParamEstim 1.10.0
[a077e3f3-b75c-5d7f-a0c6-6bc4c8ec64a9] DiffEqProblemLibrary 4.6.0
[ef61062a-5684-51dc-bb67-a0fcdec5c97d] DiffEqUncertainty 1.3.0
[0c46a032-eb83-5123-abaf-570d42b7fbaa] DifferentialEquations 6.9.0
[7073ff75-c697-5162-941a-fcdaad2a7d2a] IJulia 1.20.2
[7f56f5a3-f504-529b-bc02-0b1fe5e64312] LSODA 0.6.1
[76087f3c-5699-56af-9a33-bf431cd00edd] NLopt 0.5.1
[c030b06c-0b6d-57c2-b091-7029874bd033] ODE 2.6.0
[54ca160b-1b9f-5127-a996-1867f4bc2a2c] ODEInterface 0.4.6
[09606e27-ecf5-54fc-bb29-004bd9f985bf] ODEInterfaceDiffEq 3.5.0
[1dea7af3-3e70-54e6-95c3-0bf5283fa5ed] OrdinaryDiffEq 5.26.4
[65888b18-ceab-5e60-b2b9-181511a3b968] ParameterizedFunctions 4.2.1
[91a5bcdd-55d7-5caf-9e0b-520d859cae80] Plots 0.28.3
[b4db0fb7-de2a-5028-82bf-5021f5cfa881] ReactionNetworkImporters 0.1.5
[f2c3362d-daeb-58d1-803e-2bc74f2840b4] RecursiveFactorization 0.1.0
[9672c7b4-1e72-59bd-8a11-6ac3964bc41f] SteadyStateDiffEq 1.5.0
[c3572dad-4567-51f8-b174-8c6c989267f4] Sundials 3.8.1
[44d3d7a6-8a23-5bf8-98c5-b353f8df5ec9] Weave 0.9.1
[b77e0a4c-d291-57a0-90e8-8db25a27a240] InteractiveUtils 
[d6f4376e-aef5-505a-96c1-9c027394607a] Markdown 
[44cfe95a-1eb2-52ea-b672-e2afdf69b78f] Pkg 
[9a3f8284-a2c9-5f02-9a11-845980a1fd5c] Random